Complex Valued Nonlinear Adaptive Filters Noncircularity, Widely Linear and Neural Models

Danilo P. Mandic
Vanessa Su Lee Goh

About the Book

This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics.

This offers a number of theoretical performance gains, which is illustrated on both stochastic gradient algorithms, such as the augmented complex least mean square (ACLMS), and those based on Kalman filters. This work is supported by a number of simulations using synthetic and real world data, including the noncircular and intermittent radar and wind signals.

Brief Table of Contents

  • 1. The Magic of Complex Numbers
  • 2. Why Signal Processing in the Complex Domain?
  • 3. Adaptive Filtering Architectures
  • 4. Complex Nonlinear Activation Functions
  • 5. Elements of CR Calculus
  • 6. Complex Valued Adaptive Filters
  • 7. Adaptive Filters with Feedback
  • 8. Filters with an Adaptive Stepsize
  • 9. Filters with an Adaptive Amplitude of Nonlinearity
  • 10. Data-reusing Algorithms for Complex Valued Adaptive Filters
  • 11. Complex Mappings and Möbius Transformations
  • 12. Augmented Complex Statistics
  • 13. Widely Linear Estimation and Augmented CLMS (ACLMS)
  • 14. Duality Between Complex Valued and Real Valued Filters
  • 15. Widely Linear Filters with Feedback
  • 16. Collaborative Adaptive Filtering
  • 17. Adaptive Filtering Based on EMD
  • 18. Validation of Complex Representations: Is This Worthwhile?
  • Some typo's, mostly Section 15.4 and Section 15.5 [pdf]